Bonn States on the Cuntz Algebras and P-adic Random Walk States on the Cuntz Algebras and P-adic Random Walk States on the Cuntz Algebras and P -adic Random Walk

We study Markov measures and a p-adic random walk with the use of states on the Cuntz algebras Op. Via the GNS-construction, these come from families of representations of Op. We prove that these representations reflect self-similarity especially well. In this paper we consider a Cuntz-Krieger type algebra where the adjacency matrix depends on a parameter q (q = 1 is the case of Cuntz-Krieger). This is an ongoing work generalizing a construction of certain measures associated to random walks on graphs. Dedicated to Alan Carey, on the occasion of his 60 th birthday